International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN. 

Fuzzy reliability optimization and Performance analysis of Multi-Component Multi-Complex systems

    ,

Author Affiliations

  • 1Department of Mathematics, H. N. B. Garhwal University, B. G. R. Campus, Pauri-246001, Uttarakhand, India
  • 2Department of Mathematics, H. N. B. Garhwal University, B. G. R. Campus, Pauri-246001, Uttarakhand, India

Res. J. Mathematical & Statistical Sci., Volume 14, Issue (1), Pages 11-19, January,12 (2026)

Abstract

Multi-component multi-complex (MCMCS) are common in the engineering industry, including aerospace, power grid, transportation, and manufacturing, where reliability is a significant factor of performance and safety. Conventional methods of reliability analysis (mostly using probabilistic models) can be pretty ineffective in explaining the uncertainties that are caused by incomplete data, subjective input, and operational variability in the real world. To overcome these shortcomings, the fuzzy set theory provides a sound framework that allows one to model and optimize when facing vagueness and imprecision. This paper presents a fuzzy optimization and performance appraisal model specific to MCMCS. This methodology combines fuzzy membership functions of failure rates and repair times with multi-objective optimization procedures that optimize system reliability and availability and lessen cost and resource constraints. The given approach is practical, as evidenced by a case-based analysis that shows the improvement of the suggested method compared to the conventional probabilistic one. Sensitivity analysis also shows the model's flexibility at different uncertainty levels. The main contributions of this work are as follows: (i) a fuzzy modeling framework of complex interdependent systems is developed, (ii) the fusion of the fuzzy multi-objective optimization to enhance reliability, and (iii) a set of performance evaluation metrics can be applied to real-life engineering systems. The findings highlight the possibility of fuzzy reliability optimization to offer more realistic and practical decision-making aids used in fundamental system design and maintenance approaches.-component multi-complex (MCMCS) are common in the engineering industry, including aerospace, power grid, transportation, and manufacturing, where reliability is a significant factor of performance and safety. Conventional methods of reliability analysis (mostly using probabilistic models) can be pretty ineffective in explaining the uncertainties that are caused by incomplete data, subjective input, and operational variability in the real world. To overcome these shortcomings, the fuzzy set theory provides a sound framework, which allows one to model and optimize when facing vagueness and imprecision. This paper presents a fuzzy optimization and performance appraisal model that is specific to MCMCS. This methodology combines fuzzy membership functions of failure rates and repair times with multi-objective optimization procedures that optimize system reliability and availability and lessen cost and resource constraints. The given approach is effective, as evidenced by a case-based analysis that shows the improvement of the suggested method in comparison to the conventional probabilistic one. Sensitivity analysis also shows the model's flexibility at different uncertainty levels.

References

  1. Elsayed, E. A. (2012). Reliability engineering. John Wiley & Sons., undefined, undefined
  2. Rausand, M., & Hoyland, A. (2004). System reliability theory: Models, statistical methods, and applications. John Wiley & Sons., undefined, undefined
  3. Modarres, M. (2016). Reliability engineering and risk analysis: A practical guide. CRC Press., undefined, undefined
  4. Zio, E. (2009). Reliability engineering: Old problems and new challenges. Reliability Engineering & System Safety, 94(2), 125–141., undefined, undefined
  5. Chen, S. J., & Pham, H. (2001). Fuzzy sets and fuzzy logic in reliability engineering. CRC Press., undefined, undefined
  6. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353., undefined, undefined
  7. Kumar, U. D., Crocker, J., Knezevic, J., & El-Haram, M. (2010). Reliability, maintainability and risk. CRC Press., undefined, undefined
  8. Onisawa, T. (1990). An approach to human reliability in man-machine systems using fuzzy sets. Reliability Engineering & System Safety, 27(3), 189–202., undefined, undefined
  9. Xing, L., Amari, S. V., & Wang, X. (2016). Fuzzy Bayesian networks for system reliability analysis under epistemic uncertainty. IEEE Transactions on Reliability, 65(2), 816–829., undefined, undefined
  10. Iyer, N., & Venkatachalam, S. (2013). Reliability modeling of complex systems: Challenges and future trends. International Journal of Quality & Reliability Management, 30(3), 247–268., undefined, undefined
  11. Coit, D. W., & Smith, A. E. (1996). Reliability optimization of series–parallel systems using a genetic algorithm. IEEE Transactions on Reliability, 45(2), 254–260., undefined, undefined
  12. Zhou, X., Huang, H. Z., & Li, Y. (2018). Fuzzy multi-objective reliability optimization for complex systems. Applied Soft Computing, 65, 315–327., undefined, undefined
  13. Modarres, M. (2016). Reliability engineering and risk analysis: A practical guide. CRC Press., undefined, undefined
  14. Trivedi, K. S., & Bobbio, A. (2017). Continuous-Time Markov Chain: Reliability Models. In Reliability and Availability Engineering: Modeling, Analysis, and Applications (pp. 357–422). chapter, Cambridge: Cambridge University Press., undefined, undefined
  15. Levitin, G. (2005). The universal generating function in reliability analysis and optimization. Springer., undefined, undefined
  16. Mandal, S., & Pham, H. (2015). Reliability and availability optimization of complex systems using particle swarm optimization. Reliability Engineering & System Safety, 142, 357–364., undefined, undefined
  17. Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in Engineering Software, 69, 46–61., undefined, undefined
  18. Deb, K., Pratap, A., Agarwal, S., &Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197., undefined, undefined
  19. Cai, K. Y. (1996). Introduction to fuzzy reliability. Springer., undefined, undefined
  20. Pham, H. (2006). Reliability and optimal maintenance. Springer., undefined, undefined
  21. Billinton, R., & Allan, R. N. (1992). Reliability evaluation of engineering systems. Springer., undefined, undefined
  22. Barlow, R. E., &Proschan, F. (1975). Statistical theory of reliability and life testing. Holt, Rinehart and Winston., undefined, undefined
  23. Goel, A. L. (1985). Software reliability models: Assumptions, limitations, and applicability. IEEE Transactions on Software Engineering, 11(12), 1411–1423., undefined, undefined
  24. Park, K. S. (1987). Fuzzy-set theoretic interpretation of economic reliability. IEEE Transactions on Reliability, 36(5), 629–631., undefined, undefined
  25. Ross, T. J. (2004). Fuzzy logic with engineering applications. John Wiley & Sons., undefined, undefined
  26. Sait, S. M., & Youssef, H. (1999). Iterative computer algorithms with applications in engineering: Solving combinatorial optimization problems. IEEE Computer Society Press., undefined, undefined
  27. Yao, J., & Lin, C. (2002). Fuzzy optimization: Recent advances and applications. Springer., undefined, undefined
  28. Pham, H., & Wang, H. (1996). Imperfect maintenance. European Journal of Operational Research, 94(3), 425–438., undefined, undefined
  29. Birolini, A. (2017). Reliability engineering: Theory and practice. Springer., undefined, undefined
  30. Yang, B. (2007). Reliability, maintainability and risk: Practical methods for engineers. Butterworth-Heinemann., undefined, undefined
  31. Gupta, A., & Gupta, R. (2013). Reliability analysis of multi-component systems with fuzzy failure data. International Journal of Quality & Reliability Management, 30(3), 325–340., undefined, undefined
  32. Wang, W., & Pham, H. (2011). Reliability modeling and optimization under fuzzy environment. Applied Soft Computing, 11(1), 119–129., undefined, undefined
  33. Guo, H., & Yang, X. (2007). Fuzzy fault tree analysis of a control system. Reliability Engineering & System Safety, 92(3), 396–403., undefined, undefined
  34. Kang, R., & Zhou, X. (2012). System reliability optimization under uncertainty using fuzzy mathematics. International Journal of Performability Engineering, 8(5), 531–540., undefined, undefined
  35. Tsoukalas, L. H., & Uhrig, R. E. (1997). Fuzzy and neural approaches in engineering. John Wiley & Sons., undefined, undefined
  36. Patra, G., & Pham, H. (2014). Reliability analysis of repairable systems with fuzzy parameters. International Journal of Quality & Reliability Management, 31(2), 159–173., undefined, undefined
  37. Liu, Y., & Li, X. (2015). Reliability analysis of k-out-of-n systems with fuzzy components. Soft Computing, 19(7), 1933–1946., undefined, undefined
  38. Cheng, C. H. (1998). Evaluating weapon systems using fuzzy multi-criteria decision making. Fuzzy Sets and Systems, 100(1-3), 9–26., undefined, undefined
  39. Murthy, D. N. P., & Nguyen, D. (1985). System reliability under fuzzy environments. IEEE Transactions on Reliability, 34(5), 473–478., undefined, undefined
  40. Zhao, Y., & Liu, H. (2013). Reliability allocation for complex systems under fuzzy constraints. Reliability Engineering & System Safety, 116, 78–87., undefined, undefined
  41. Huang, H. Z., & Zuo, M. J. (2000). Optimization of system reliability using fuzzy numbers. Computers & Industrial Engineering, 38(2), 357–372., undefined, undefined
  42. Lin, C., & Yao, J. (2003). Fuzzy linear programming models for reliability design. Fuzzy Sets and Systems, 139(3), 395–414., undefined, undefined
  43. Misra, K. B. (1992). Reliability analysis and prediction: A methodology oriented treatment. Elsevier., undefined, undefined
  44. Zhu, Q., & Chen, X. (2007). Reliability modeling with uncertain failure data. Applied Mathematics and Computation, 185(1), 23–34., undefined, undefined
  45. Jain, R., & Garg, H. (2018). A novel reliability measure of a system with complex structure using intuitionistic fuzzy set. IEEE Transactions on Fuzzy Systems, 26(4), 2130–2137., undefined, undefined
  46. Li, X., & Huang, H. Z. (2008). Fuzzy lifetime data analysis and reliability estimation. International Journal of Reliability, Quality and Safety Engineering, 15(4), 323–339., undefined, undefined
  47. Garg, H., & Sharma, S. (2012). Multi-objective reliability-redundancy allocation problem using fuzzy goal programming. Computers & Industrial Engineering, 62(4), 1091–1100., undefined, undefined
  48. Singh, C., &Billinton, R. (1977). System reliability modeling and evaluation. Hutchinson Ross., undefined, undefined
  49. Zuo, M. J., & Cui, L. (2003). Reliability evaluation of multi-state systems using fuzzy sets. IEEE Transactions on Reliability, 52(2), 181–187., undefined, undefined
  50. Mahapatra, G. S., & Roy, T. K. (2009). Reliability evaluation using fuzzy failure rates. Applied Mathematical Modelling, 33(1), 146–157., undefined, undefined
  51. Gupta, R., & Sharma, A. (2011). Reliability analysis of communication networks under fuzzy environment. International Journal of Performability Engineering, 7(2), 171–182., undefined, undefined
  52. Singh, V., & Yadav, O. P. (2013). Reliability-based design optimization under fuzzy uncertainty. Quality and Reliability Engineering International, 29(3), 365–375., undefined, undefined
  53. Xu, J., Zhan, T., & Deng, Y. (2025). Evaluating evidential reliability in pattern recognition based on intuitionistic fuzzy sets. International Journal of Fuzzy Systems, 1-15., undefined, undefined
  54. Kamal, M., Modibbo, U. M., AlArjani, A., & Ali, I. (2021). Neutrosophic fuzzy goal programming approach in selective maintenance allocation of system reliability. Complex & intelligent systems, 7(2), 1045-1059., undefined, undefined
  55. Sharma, H. L., Shukla, V., & Shukla, V. (2025). A genetic algorithm approach for optimization problems. Research Journal of Mathematical & Statistical Sciences, 13(3), 14–19., undefined, undefined